
## Setup
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import warnings
warnings.simplefilter('ignore', DeprecationWarning)
%matplotlib inline
import seaborn as sns
import plotly.express as px
import scipy.stats as stats

# Import Cluster Analysis libraries
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler, normalize
from sklearn.preprocessing import MinMaxScaler, LabelEncoder
from sklearn.decomposition import PCA
from sklearn.cluster import KMeans, DBSCAN, AgglomerativeClustering
from sklearn import metrics
from sklearn.neighbors import NearestNeighbors
import scipy.cluster.hierarchy as sch

#import visualization libraries
from matplotlib.pyplot import scatter
import plotly
from plotly.graph_objs import Scatter, Marker, Layout, layout,XAxis, YAxis, Bar, Line
%matplotlib inline

# get ANOVA table as R like output
import statsmodels.api as sm
from statsmodels.formula.api import ols


# load the airline satisfaction  dataset

df = pd.read_csv('https://raw.githubusercontent.com/dk28yip/MSDS7331/main/airline.csv') # read in the csv file
df.head()

#reduced samples set from 100,000 to 30,000 as a few of us had computer performance issues
df = df.sample(n=30000)


# Any missing values in the dataset
def plot_missingness(df: pd.DataFrame=df) -> None:
    nan_df = pd.DataFrame(df.isna().sum()).reset_index()
    nan_df.columns  = ['Column', 'NaN_Count']
    nan_df['NaN_Count'] = nan_df['NaN_Count'].astype('int')
    nan_df['NaN_%'] = round(nan_df['NaN_Count']/df.shape[0] * 100,4)
    nan_df['Type']  = 'Missingness'
    nan_df.sort_values('NaN_%', inplace=True)

    # Add completeness
    for i in range(nan_df.shape[0]):
        complete_df = pd.DataFrame([nan_df.loc[i,'Column'],df.shape[0] - nan_df.loc[i,'NaN_Count'],100 - nan_df.loc[i,'NaN_%'], 'Completeness']).T
        complete_df.columns  = ['Column','NaN_Count','NaN_%','Type']
        complete_df['NaN_%'] = complete_df['NaN_%'].astype('int')
        complete_df['NaN_Count'] = complete_df['NaN_Count'].astype('int')
        nan_df = pd.concat([nan_df,complete_df], sort=True)
            
    nan_df = nan_df.rename(columns={"Column": "Feature", "NaN_%": "Missing %"})

    # Missingness Plot
    fig = px.bar(nan_df,
                 x='Feature',
                 y='Missing %',
                 title=f"Missingness Plot (N={df.shape[0]})",
                 color='Type',
                 opacity = 0.6,
                 color_discrete_sequence=['red','#808080'],
                 width=800,
                 height=800)
    fig.show()

plot_missingness(df)

print("Missing 99 values if the 'Arrival Delay in Minutes'column; approximately 0.31%.")

Missing 99 values if the 'Arrival Delay in Minutes'column; approximately 0.31%.


df["GenderNumeric"] = (df["Gender"]=="Male").astype(int)
df["CustomerTypeNumeric"] = (df["Customer Type"]=="Loyal Customer").astype(int)
df["TypeofTravelNumeric"] = (df["Type of Travel"]=="Personal Travel").astype(int)
df["ClassNumeric"] = df["Class"]
df["ClassNumeric"].replace(['Eco', 'Eco Plus', 'Business'], [0, 1, 2], inplace=True)
#Change Satisfaction to 1 or 0
df["SatisfactionNumeric"] = df["satisfaction"]
df["SatisfactionNumeric"].replace(['neutral or dissatisfied', 'satisfied'], [0,1], inplace = True)


df["Arrival Delay in Minutes"]= df["Arrival Delay in Minutes"].fillna(0)


dfclean = df.drop(columns=['id'])

dfclean.isnull().sum() #double check on the missing values - 'arrival delay in minutes =310'

Gender                               0
Customer Type                        0
Age                                  0
Type of Travel                       0
Class                                0
Flight Distance                      0
Inflight wifi service                0
Departure/Arrival time convenient    0
Ease of Online booking               0
Gate location                        0
Food and drink                       0
Online boarding                      0
Seat comfort                         0
Inflight entertainment               0
On-board service                     0
Leg room service                     0
Baggage handling                     0
Checkin service                      0
Inflight service                     0
Cleanliness                          0
Departure Delay in Minutes           0
Arrival Delay in Minutes             0
satisfaction                         0
GenderNumeric                        0
CustomerTypeNumeric                  0
TypeofTravelNumeric                  0
ClassNumeric                         0
SatisfactionNumeric                  0
dtype: int64


#Fill in missing values
dfclean["Arrival Delay in Minutes"].fillna(dfclean["Arrival Delay in Minutes"].median(), inplace=True)


dfclean.describe().T


dfclean.corr()


f, ax = plt.subplots(figsize=[18, 13])
sns.heatmap(dfclean.corr(), annot=True, fmt=".2f", ax=ax, cmap="bwr")
ax.set_title("Correlation Matrix", fontsize=20)
plt.show()


##distribution of the data

for column in dfclean:
    
    sns.displot(x=column, data=dfclean)

C:\Users\thud1\anaconda3\envs\ML7331\lib\site-packages\seaborn\axisgrid.py:409: RuntimeWarning:

More than 20 figures have been opened. Figures created through the pyplot interface (`matplotlib.pyplot.figure`) are retained until explicitly closed and may consume too much memory. (To control this warning, see the rcParam `figure.max_open_warning`).


print (dfclean.info())

<class 'pandas.core.frame.DataFrame'>
Int64Index: 30000 entries, 42798 to 27683
Data columns (total 28 columns):
 #   Column                             Non-Null Count  Dtype  
---  ------                             --------------  -----  
 0   Gender                             30000 non-null  object 
 1   Customer Type                      30000 non-null  object 
 2   Age                                30000 non-null  int64  
 3   Type of Travel                     30000 non-null  object 
 4   Class                              30000 non-null  object 
 5   Flight Distance                    30000 non-null  int64  
 6   Inflight wifi service              30000 non-null  int64  
 7   Departure/Arrival time convenient  30000 non-null  int64  
 8   Ease of Online booking             30000 non-null  int64  
 9   Gate location                      30000 non-null  int64  
 10  Food and drink                     30000 non-null  int64  
 11  Online boarding                    30000 non-null  int64  
 12  Seat comfort                       30000 non-null  int64  
 13  Inflight entertainment             30000 non-null  int64  
 14  On-board service                   30000 non-null  int64  
 15  Leg room service                   30000 non-null  int64  
 16  Baggage handling                   30000 non-null  int64  
 17  Checkin service                    30000 non-null  int64  
 18  Inflight service                   30000 non-null  int64  
 19  Cleanliness                        30000 non-null  int64  
 20  Departure Delay in Minutes         30000 non-null  int64  
 21  Arrival Delay in Minutes           30000 non-null  float64
 22  satisfaction                       30000 non-null  object 
 23  GenderNumeric                      30000 non-null  int32  
 24  CustomerTypeNumeric                30000 non-null  int32  
 25  TypeofTravelNumeric                30000 non-null  int32  
 26  ClassNumeric                       30000 non-null  int64  
 27  SatisfactionNumeric                30000 non-null  int64  
dtypes: float64(1), int32(3), int64(19), object(5)
memory usage: 7.3+ MB
None


 #Sum Survey Score Columns - index(6:19)
dfclean['Survey_Total']=dfclean.iloc[:,6:19].sum(axis=1)

#Add Age Groups
dfclean['Age_Group'] = pd.cut(dfclean['Age'], bins = [0,17,35,65,90], labels=["Adolescent", "Young Adult", "Middle Age", "Senior"], right=True)
dfclean['Age_Group_Numeric'] = pd.cut(dfclean['Age'], bins = [0,17,35,65,90], labels=["1", "2", "3", "4"], right=True)

#Add Distance Groups
dfclean['Distance_Group'] = pd.cut(dfclean['Flight Distance'], bins = [0,500,1000,2500,5000], labels=["Short", "Moderate", "Long", "Extra Long"], right=True)
dfclean['Distance_Group_Numeric'] = pd.cut(dfclean['Flight Distance'], bins = [0,500,1000,2500,5000], labels=["1", "2", "3", "4"], right=True)

#Add Departure Delay Groups
dfclean['Departure_Delay_Group'] = pd.cut(dfclean['Departure Delay in Minutes'], bins = [-1,1,100,1600], labels=["None","Minimal","Long"], right=True)
dfclean['Departure_Delay_Group_Numeric'] = pd.cut(dfclean['Departure Delay in Minutes'], bins = [-1,1,100,1600], labels=["0","1","2"], right=True)




dfclean.head(n=50)


#Plotly Histogram - Age
px.histogram(dfclean['Age'], x= "Age",
             title = 'Age Distribution',
             )


#Plotly Histogram - Flight Distance
px.histogram(dfclean['Flight Distance'], x= "Flight Distance",
             title = 'Flight Distance Distribution',
             )


#Plotly Histogram - Departure Delay in Minutes
px.histogram(dfclean['Departure Delay in Minutes'], x= "Departure Delay in Minutes",
             title = 'Departure Delay Distribution',
             nbins = 50,
             )


#Plotly Histogram - Arrival Delay in Minutes
px.histogram(dfclean['Arrival Delay in Minutes'], x= "Arrival Delay in Minutes",
             title = 'Arrival Delay Distribution',
             nbins = 50,
             )


px.box(dfclean,
       x="Class", y="Age", 
       color="Class",
       title = "Box Plot of Age by Class")


#ANOVA of class to age
# Ordinary Least Squares (OLS) model
model = ols('Age ~ C(Class)', data=dfclean).fit()
anova_table = sm.stats.anova_lm(model, typ=2)
anova_table


px.box(dfclean,
       x="Class", y="Survey_Total", 
       color="Class",
       title = "Box Plot of Survey Total by Class")


#ANOVA of Class to Total Survey Score
# Ordinary Least Squares (OLS) model
model = ols('Survey_Total ~ C(Class)', data=dfclean).fit()
anova_table = sm.stats.anova_lm(model, typ=2)
anova_table


px.box(dfclean,
       x="Distance_Group", y="Survey_Total", 
       color="Distance_Group",
       title = "Box Plot of Distance Traveled by Survey Total")


#ANOVA of age to Total Survey Score
# Ordinary Least Squares (OLS) model
model = ols('Survey_Total ~ C(Distance_Group)', data=dfclean).fit()
anova_table = sm.stats.anova_lm(model, typ=2)
anova_table


#ANOVA of class to Total Survey Score
# Ordinary Least Squares (OLS) model
model = ols('Survey_Total ~ C(Age)', data=dfclean).fit()
anova_table = sm.stats.anova_lm(model, typ=2)
anova_table


px.box(dfclean,
       x="Departure_Delay_Group", y="Survey_Total", 
       color="Departure_Delay_Group",
       title = "Box Plot of Total by Departure Delay Group")


#ANOVA of age to Total Survey Score
# Ordinary Least Squares (OLS) model
model = ols('Survey_Total ~ C(Departure_Delay_Group)', data=dfclean).fit()
anova_table = sm.stats.anova_lm(model, typ=2)
anova_table


#2 Sample T-Test - Male vs Female

# Subset data
male = dfclean.query('Gender == "Male"')['Survey_Total']
female = dfclean.query('Gender == "Female"')['Survey_Total']

dfclean.groupby('Gender').describe()


#Check normality assumption

#Plotly Histogram - Total
px.histogram(dfclean, x= "Survey_Total",
             title = 'Survey Total Distribution',
             facet_col="Gender"
             )


#Check Variance Assumptions
stats.levene(male, female)

LeveneResult(statistic=3.970966701611184, pvalue=0.046300234377207254)


#T-Test
res = stats.ttest_ind(male, female, equal_var=True)

display(res)

Ttest_indResult(statistic=0.3458585763053265, pvalue=0.7294514263123113)


#set data to be ready for cluster analysis
cluster_df = dfclean.copy()

continuous_features = ['Flight Distance','Departure Delay in Minutes','Arrival Delay in Minutes']

# and the oridnal values to be integers
ordinal_features = ['Age','Inflight wifi service','Departure/Arrival time convenient']

# we won't touch these variables, keep them as categorical
categ_features = ['GenderNumeric','TypeofTravelNumeric','CustomerTypeNumeric', 'SatisfactionNumeric'];

# use the "astype" function to change the variable type
cluster_df[continuous_features] = cluster_df[continuous_features].astype(np.float64)
cluster_df[ordinal_features] = cluster_df[ordinal_features].astype(np.int64)
cluster_df = cluster_df.drop(['Age_Group','Distance_Group','Distance_Group_Numeric','Gender','Customer Type','Type of Travel', 'Class','Departure_Delay_Group','Departure_Delay_Group_Numeric','Age_Group_Numeric', 'satisfaction'], axis=1)


cluster_df.info() # now our data looks better!!

<class 'pandas.core.frame.DataFrame'>
Int64Index: 30000 entries, 16096 to 86438
Data columns (total 24 columns):
 #   Column                             Non-Null Count  Dtype  
---  ------                             --------------  -----  
 0   Age                                30000 non-null  int64  
 1   Flight Distance                    30000 non-null  float64
 2   Inflight wifi service              30000 non-null  int64  
 3   Departure/Arrival time convenient  30000 non-null  int64  
 4   Ease of Online booking             30000 non-null  int64  
 5   Gate location                      30000 non-null  int64  
 6   Food and drink                     30000 non-null  int64  
 7   Online boarding                    30000 non-null  int64  
 8   Seat comfort                       30000 non-null  int64  
 9   Inflight entertainment             30000 non-null  int64  
 10  On-board service                   30000 non-null  int64  
 11  Leg room service                   30000 non-null  int64  
 12  Baggage handling                   30000 non-null  int64  
 13  Checkin service                    30000 non-null  int64  
 14  Inflight service                   30000 non-null  int64  
 15  Cleanliness                        30000 non-null  int64  
 16  Departure Delay in Minutes         30000 non-null  float64
 17  Arrival Delay in Minutes           30000 non-null  float64
 18  GenderNumeric                      30000 non-null  int32  
 19  CustomerTypeNumeric                30000 non-null  int32  
 20  TypeofTravelNumeric                30000 non-null  int32  
 21  ClassNumeric                       30000 non-null  int64  
 22  SatisfactionNumeric                30000 non-null  int64  
 23  Survey_Total                       30000 non-null  int64  
dtypes: float64(3), int32(3), int64(18)
memory usage: 6.4 MB


#scale values
cluster_df_scaled = StandardScaler().fit(cluster_df).transform(cluster_df.astype(float))


# finding optimal cluster amount
wcss = []
for i in range(1,20):
   model = KMeans(n_clusters = i, init = "k-means++", random_state=50)
   model.fit(cluster_df_scaled)
   wcss.append(model.inertia_)
plt.figure(figsize=(10,10))
plt.plot(range(1,20), wcss)
plt.xlabel('Number of clusters')
plt.ylabel('WCSS')
plt.show()


# reducing dimensionality and create new data based on our PCA.
pca = PCA(2)
data = pca.fit_transform(cluster_df_scaled)
data

array([[ 1.84267024, -2.00373957],
       [ 2.20544825, -0.90255478],
       [ 0.088318  , -1.11898053],
       ...,
       [ 4.19832338,  0.55916796],
       [-0.19883972,  2.05908113],
       [ 2.00110632,  0.19032105]])


# clustering with PCA components

model = KMeans(n_clusters = 8, init = "k-means++")
label = model.fit_predict(data)


plt.figure(figsize=(10,10))
uniq = np.unique(label)
for i in uniq:
   plt.scatter(data[label == i , 0] , data[label == i , 1] , label = i)


plt.legend()
plt.title('KMeans Clustering', fontsize=15)
plt.show()


metrics.silhouette_score(cluster_df_scaled, label)

0.04467975673601045


neigh = NearestNeighbors(n_neighbors=2)
nbrs = neigh.fit(data)
distances, indices = nbrs.kneighbors(data)

distances = np.sort(distances, axis=0)
distances = distances[:,1]
plt.plot(distances)

[<matplotlib.lines.Line2D at 0x29ae75181c0>]


# DBScan Clustering with PCA

dbscan = DBSCAN(eps=0.2)
dbscan_label = dbscan.fit_predict(data)

plt.figure(figsize=(10,10))
uniq = np.unique(dbscan_label)
for i in uniq:
   plt.scatter(data[label == i , 0] , data[label == i , 1] , label = i)


plt.legend()
plt.title('DBSCAN Clustering', fontsize=15)
plt.show()


metrics.silhouette_score(cluster_df_scaled, dbscan_label)

-0.0652248129630493


# utilizing a dendrogram to find the optimal number of clusters

dendrogram = sch.dendrogram(sch.linkage(data, method='ward'))
plt.title('Dendrogram')
plt.show()


hac = AgglomerativeClustering(n_clusters=5, affinity='euclidean',linkage='ward')
hac_label = hac.fit_predict(data)

plt.figure(figsize=(10,10))
uniq = np.unique(hac_label)
for i in uniq:
    plt.scatter(data[label == i , 0] , data[label == i , 1] , label = i)


plt.legend()
plt.title('HAC Clustering', fontsize=15)
plt.show()


metrics.silhouette_score(cluster_df_scaled, hac_label)

0.07435444471933086


result_df = dfclean.copy()
result_df['kmeans_cluster'] = label
result_df['dbscan_cluster'] = dbscan_label
result_df['hac_cluster'] = hac_label
result_df.info()

<class 'pandas.core.frame.DataFrame'>
Int64Index: 30000 entries, 16096 to 86438
Data columns (total 38 columns):
 #   Column                             Non-Null Count  Dtype   
---  ------                             --------------  -----   
 0   Gender                             30000 non-null  object  
 1   Customer Type                      30000 non-null  object  
 2   Age                                30000 non-null  int64   
 3   Type of Travel                     30000 non-null  object  
 4   Class                              30000 non-null  object  
 5   Flight Distance                    30000 non-null  int64   
 6   Inflight wifi service              30000 non-null  int64   
 7   Departure/Arrival time convenient  30000 non-null  int64   
 8   Ease of Online booking             30000 non-null  int64   
 9   Gate location                      30000 non-null  int64   
 10  Food and drink                     30000 non-null  int64   
 11  Online boarding                    30000 non-null  int64   
 12  Seat comfort                       30000 non-null  int64   
 13  Inflight entertainment             30000 non-null  int64   
 14  On-board service                   30000 non-null  int64   
 15  Leg room service                   30000 non-null  int64   
 16  Baggage handling                   30000 non-null  int64   
 17  Checkin service                    30000 non-null  int64   
 18  Inflight service                   30000 non-null  int64   
 19  Cleanliness                        30000 non-null  int64   
 20  Departure Delay in Minutes         30000 non-null  int64   
 21  Arrival Delay in Minutes           30000 non-null  float64 
 22  satisfaction                       30000 non-null  object  
 23  GenderNumeric                      30000 non-null  int32   
 24  CustomerTypeNumeric                30000 non-null  int32   
 25  TypeofTravelNumeric                30000 non-null  int32   
 26  ClassNumeric                       30000 non-null  int64   
 27  SatisfactionNumeric                30000 non-null  int64   
 28  Survey_Total                       30000 non-null  int64   
 29  Age_Group                          30000 non-null  category
 30  Age_Group_Numeric                  30000 non-null  category
 31  Distance_Group                     30000 non-null  category
 32  Distance_Group_Numeric             30000 non-null  category
 33  Departure_Delay_Group              30000 non-null  category
 34  Departure_Delay_Group_Numeric      30000 non-null  category
 35  kmeans_cluster                     30000 non-null  int32   
 36  dbscan_cluster                     30000 non-null  int64   
 37  hac_cluster                        30000 non-null  int64   
dtypes: category(6), float64(1), int32(4), int64(22), object(5)
memory usage: 8.3+ MB


# clusters compared to Gender
fig, axes = plt.subplots(1, 3, figsize=(15, 5), sharey=True)
fig.suptitle('Clustering Methods and Flight Distance')

# Kmeans
sns.boxplot(ax=axes[0], x=result_df['kmeans_cluster'].values, y=result_df['Flight Distance'].values)
axes[0].set_title('KMeans')

# DBSCAN
sns.boxplot(ax=axes[1], x=result_df['dbscan_cluster'].values, y=result_df['Flight Distance'].values)
axes[1].set_title('DBSCAN')

# HAC
sns.boxplot(ax=axes[2], x=result_df['hac_cluster'].values, y=result_df['Flight Distance'].values)
axes[2].set_title('HAC')

Text(0.5, 1.0, 'HAC')


# clusters compared to Survey Total
fig, axes = plt.subplots(1, 3, figsize=(15, 5), sharey=True)
fig.suptitle('Clustering Methods and Gender')

# Kmeans
sns.boxplot(ax=axes[0], x=result_df['kmeans_cluster'].values, y=result_df['Survey_Total'].values)
axes[0].set_title('KMeans')

# DBSCAN
sns.boxplot(ax=axes[1], x=result_df['dbscan_cluster'].values, y=result_df['Survey_Total'].values)
axes[1].set_title('DBSCAN')

# HAC
sns.boxplot(ax=axes[2], x=result_df['hac_cluster'].values, y=result_df['Survey_Total'].values)
axes[2].set_title('HAC')

Text(0.5, 1.0, 'HAC')


from sklearn.preprocessing import StandardScaler, normalize
from sklearn.decomposition import PCA
from sklearn.mixture import GaussianMixture 
from sklearn.metrics import silhouette_score
from sklearn.model_selection import train_test_split
from sklearn import metrics


cluster_df.info()

<class 'pandas.core.frame.DataFrame'>
Int64Index: 30000 entries, 16096 to 86438
Data columns (total 24 columns):
 #   Column                             Non-Null Count  Dtype  
---  ------                             --------------  -----  
 0   Age                                30000 non-null  int64  
 1   Flight Distance                    30000 non-null  float64
 2   Inflight wifi service              30000 non-null  int64  
 3   Departure/Arrival time convenient  30000 non-null  int64  
 4   Ease of Online booking             30000 non-null  int64  
 5   Gate location                      30000 non-null  int64  
 6   Food and drink                     30000 non-null  int64  
 7   Online boarding                    30000 non-null  int64  
 8   Seat comfort                       30000 non-null  int64  
 9   Inflight entertainment             30000 non-null  int64  
 10  On-board service                   30000 non-null  int64  
 11  Leg room service                   30000 non-null  int64  
 12  Baggage handling                   30000 non-null  int64  
 13  Checkin service                    30000 non-null  int64  
 14  Inflight service                   30000 non-null  int64  
 15  Cleanliness                        30000 non-null  int64  
 16  Departure Delay in Minutes         30000 non-null  float64
 17  Arrival Delay in Minutes           30000 non-null  float64
 18  GenderNumeric                      30000 non-null  int32  
 19  CustomerTypeNumeric                30000 non-null  int32  
 20  TypeofTravelNumeric                30000 non-null  int32  
 21  ClassNumeric                       30000 non-null  int64  
 22  SatisfactionNumeric                30000 non-null  int64  
 23  Survey_Total                       30000 non-null  int64  
dtypes: float64(3), int32(3), int64(18)
memory usage: 6.4 MB


# Standardize data
scaler = StandardScaler() 
scaled_df = scaler.fit_transform(cluster_df) 
  
# Normalizing the Data 
normalized_df = normalize(scaled_df) 
  
# Converting the numpy array into a pandas DataFrame 
normalized_df = pd.DataFrame(normalized_df)


n_range = range(2,20)

# Create empty lists to store the BIC and AIC values
bic_score = []
aic_score = []

for n in n_range:
    gm = GaussianMixture(n_components=n, 
                         random_state=123, 
                         n_init=10)
    gm.fit(normalized_df)
    
    # Append the BIC and AIC to the respective lists
    bic_score.append(gm.bic(normalized_df))
    aic_score.append(gm.aic(normalized_df))


fig, ax = plt.subplots(figsize=(12,8),nrows=1)
ax.plot(n_range, bic_score, '-o', color='orange')
ax.plot(n_range, aic_score, '-o', color='green')
ax.set(xlabel='Number of Clusters', ylabel='Score')
ax.set_xticks(n_range)
ax.set_title('BIC and AIC Scores Per Number Of Clusters')

Text(0.5, 1.0, 'BIC and AIC Scores Per Number Of Clusters')


# Reducing the dimensions of the data 
pca = PCA(n_components = 2) 
X_principal = pca.fit_transform(normalized_df) 
X_principal = pd.DataFrame(X_principal) 
X_principal.columns = ['P1', 'P2'] 
  
X_principal.head(2)

gmm = GaussianMixture(n_components = 8) 
gmm.fit(X_principal)

GaussianMixture(n_components=8)

GaussianMixture(n_components=8)


# Visualizing the clustering 
plt.scatter(X_principal['P1'], X_principal['P2'],  
           c = GaussianMixture(n_components = 8).fit_predict(X_principal), cmap =plt.cm.spring, alpha = 0.6) 
plt.show()


n_range = range(2,11)

# Create empty lists to store the BIC and AIC values
bic_score = []
aic_score = []

for n in n_range:
    gm = GaussianMixture(n_components=n, 
                         random_state=123, 
                         n_init=10)
    gm.fit(X_principal)
    
    # Append the BIC and AIC to the respective lists
    bic_score.append(gm.bic(X_principal))
    aic_score.append(gm.aic(X_principal))


fig, ax = plt.subplots(figsize=(12,8),nrows=1)
ax.plot(n_range, bic_score, '-o', color='orange')
ax.plot(n_range, aic_score, '-o', color='green')
ax.set(xlabel='Number of Clusters', ylabel='Score')
ax.set_xticks(n_range)
ax.set_title('BIC and AIC Scores Per Number Of Clusters')

Text(0.5, 1.0, 'BIC and AIC Scores Per Number Of Clusters')

	count	mean	std	min	25%	50%	75%	max
Age	30000.0	39.299833	15.138575	7.0	27.0	40.0	51.0	85.0
Flight Distance	30000.0	1183.915033	993.241471	31.0	413.0	837.0	1727.0	4983.0
Inflight wifi service	30000.0	2.736200	1.324060	0.0	2.0	3.0	4.0	5.0
Departure/Arrival time convenient	30000.0	3.055433	1.526577	0.0	2.0	3.0	4.0	5.0
Ease of Online booking	30000.0	2.762267	1.399172	0.0	2.0	3.0	4.0	5.0
Gate location	30000.0	2.971367	1.279271	0.0	2.0	3.0	4.0	5.0
Food and drink	30000.0	3.203200	1.330903	0.0	2.0	3.0	4.0	5.0
Online boarding	30000.0	3.259167	1.346771	0.0	2.0	3.0	4.0	5.0
Seat comfort	30000.0	3.441400	1.321750	1.0	2.0	4.0	5.0	5.0
Inflight entertainment	30000.0	3.359267	1.335160	0.0	2.0	4.0	4.0	5.0
On-board service	30000.0	3.390300	1.286139	1.0	2.0	4.0	4.0	5.0
Leg room service	30000.0	3.353633	1.311907	0.0	2.0	4.0	4.0	5.0
Baggage handling	30000.0	3.634367	1.184480	1.0	3.0	4.0	5.0	5.0
Checkin service	30000.0	3.310167	1.261566	1.0	3.0	3.0	4.0	5.0
Inflight service	30000.0	3.650567	1.175092	1.0	3.0	4.0	5.0	5.0
Cleanliness	30000.0	3.289867	1.313964	0.0	2.0	3.0	4.0	5.0
Departure Delay in Minutes	30000.0	14.587367	37.485305	0.0	0.0	0.0	13.0	1592.0
Arrival Delay in Minutes	30000.0	14.876867	37.744196	0.0	0.0	0.0	13.0	1584.0
GenderNumeric	30000.0	0.491900	0.499943	0.0	0.0	0.0	1.0	1.0
CustomerTypeNumeric	30000.0	0.818067	0.385796	0.0	1.0	1.0	1.0	1.0
TypeofTravelNumeric	30000.0	0.309533	0.462309	0.0	0.0	0.0	1.0	1.0
ClassNumeric	30000.0	1.029267	0.961513	0.0	0.0	1.0	2.0	2.0
SatisfactionNumeric	30000.0	0.434633	0.495717	0.0	0.0	0.0	1.0	1.0

	Age	Flight Distance	Inflight wifi service	Departure/Arrival time convenient	Ease of Online booking	Gate location	Food and drink	Online boarding	Seat comfort	Inflight entertainment	...	Checkin service	Inflight service	Cleanliness	Departure Delay in Minutes	Arrival Delay in Minutes	GenderNumeric	CustomerTypeNumeric	TypeofTravelNumeric	ClassNumeric	SatisfactionNumeric
Age	1.000000	0.100593	0.003958	0.030369	0.013305	-0.009106	0.022379	0.199120	0.165753	0.082095	...	0.030686	-0.046155	0.055864	-0.010463	-0.013109	0.000808	0.285067	-0.048445	0.139015	0.131959
Flight Distance	0.100593	1.000000	-0.000385	-0.021131	0.062276	-0.001263	0.055368	0.209287	0.162458	0.127695	...	0.069235	0.059287	0.092476	-0.001503	-0.005201	-0.000801	0.222738	-0.262669	0.445825	0.294396
Inflight wifi service	0.003958	-0.000385	1.000000	0.348631	0.713397	0.339447	0.129750	0.453095	0.120003	0.209892	...	0.039147	0.122411	0.126899	-0.019791	-0.020471	0.005182	0.001839	-0.103161	0.036542	0.282816
Departure/Arrival time convenient	0.030369	-0.021131	0.348631	1.000000	0.441277	0.451814	-0.001164	0.076496	0.012538	-0.008201	...	0.091393	0.079052	0.012031	0.003782	0.001855	0.005371	0.204754	0.261917	-0.095647	-0.057916
Ease of Online booking	0.013305	0.062276	0.713397	0.441277	1.000000	0.461168	0.025925	0.401942	0.027057	0.040868	...	0.007783	0.041945	0.011411	-0.006769	-0.008291	-0.004421	0.014664	-0.130555	0.100865	0.166857
Gate location	-0.009106	-0.001263	0.339447	0.451814	0.461168	1.000000	-0.007723	0.002373	0.002113	0.001807	...	-0.037831	0.010574	-0.006406	0.010107	0.008999	-0.008520	-0.005085	-0.024355	-0.004630	-0.003030
Food and drink	0.022379	0.055368	0.129750	-0.001164	0.025925	-0.007723	1.000000	0.227616	0.571047	0.620251	...	0.082793	0.034021	0.654333	-0.029145	-0.029670	0.011091	0.063238	-0.061811	0.088374	0.206472
Online boarding	0.199120	0.209287	0.453095	0.076496	0.401942	0.002373	0.227616	1.000000	0.421061	0.283294	...	0.203660	0.080922	0.328658	-0.019264	-0.018953	-0.047702	0.182496	-0.219595	0.320012	0.501488
Seat comfort	0.165753	0.162458	0.120003	0.012538	0.027057	0.002113	0.571047	0.421061	1.000000	0.611922	...	0.188210	0.075164	0.678665	-0.020214	-0.019982	-0.025361	0.160301	-0.117333	0.222306	0.346646
Inflight entertainment	0.082095	0.127695	0.209892	-0.008201	0.040868	0.001807	0.620251	0.283294	0.611922	1.000000	...	0.117732	0.409977	0.692659	-0.029836	-0.032594	0.010702	0.113825	-0.142957	0.193357	0.396598
On-board service	0.058279	0.106771	0.126215	0.066756	0.044895	-0.020336	0.047940	0.159393	0.127334	0.415289	...	0.241526	0.552500	0.116082	-0.033152	-0.038396	0.012564	0.050134	-0.059781	0.216732	0.320444
Leg room service	0.036321	0.134119	0.164493	0.011050	0.111251	-0.001415	0.028795	0.128322	0.101217	0.299136	...	0.149636	0.365369	0.094268	0.018398	0.016444	0.036565	0.040909	-0.146079	0.209177	0.316000
Baggage handling	-0.047479	0.063869	0.123945	0.071179	0.043150	0.010316	0.030490	0.089077	0.077582	0.380983	...	0.227521	0.627786	0.095130	-0.000621	-0.004204	0.040792	-0.029370	-0.032856	0.159693	0.245168
Checkin service	0.030686	0.069235	0.039147	0.091393	0.007783	-0.037831	0.082793	0.203660	0.188210	0.117732	...	1.000000	0.230424	0.170122	-0.010827	-0.011282	0.012202	0.026635	0.014505	0.148964	0.230787
Inflight service	-0.046155	0.059287	0.122411	0.079052	0.041945	0.010574	0.034021	0.080922	0.075164	0.409977	...	0.230424	1.000000	0.092114	-0.052596	-0.057721	0.042363	-0.023618	-0.023941	0.155858	0.244252
Cleanliness	0.055864	0.092476	0.126899	0.012031	0.011411	-0.006406	0.654333	0.328658	0.678665	0.692659	...	0.170122	0.092114	1.000000	-0.012302	-0.011373	0.007837	0.086413	-0.074011	0.134180	0.305447
Departure Delay in Minutes	-0.010463	-0.001503	-0.019791	0.003782	-0.006769	0.010107	-0.029145	-0.019264	-0.020214	-0.029836	...	-0.010827	-0.052596	-0.012302	1.000000	0.957879	0.002560	-0.008902	-0.004886	-0.012730	-0.048815
Arrival Delay in Minutes	-0.013109	-0.005201	-0.020471	0.001855	-0.008291	0.008999	-0.029670	-0.018953	-0.019982	-0.032594	...	-0.011282	-0.057721	-0.011373	0.957879	1.000000	0.000762	-0.008782	-0.005791	-0.015227	-0.053898
GenderNumeric	0.000808	-0.000801	0.005182	0.005371	-0.004421	-0.008520	0.011091	-0.047702	-0.025361	0.010702	...	0.012202	0.042363	0.007837	0.002560	0.000762	1.000000	0.023814	0.004935	0.004723	0.013601
CustomerTypeNumeric	0.285067	0.222738	0.001839	0.204754	0.014664	-0.005085	0.063238	0.182496	0.160301	0.113825	...	0.026635	-0.023618	0.086413	-0.008902	-0.008782	0.023814	1.000000	0.308275	0.106015	0.181662
TypeofTravelNumeric	-0.048445	-0.262669	-0.103161	0.261917	-0.130555	-0.024355	-0.061811	-0.219595	-0.117333	-0.142957	...	0.014505	-0.023941	-0.074011	-0.004886	-0.005791	0.004935	0.308275	1.000000	-0.541338	-0.454110
ClassNumeric	0.139015	0.445825	0.036542	-0.095647	0.100865	-0.004630	0.088374	0.320012	0.222306	0.193357	...	0.148964	0.155858	0.134180	-0.012730	-0.015227	0.004723	0.106015	-0.541338	1.000000	0.498255
SatisfactionNumeric	0.131959	0.294396	0.282816	-0.057916	0.166857	-0.003030	0.206472	0.501488	0.346646	0.396598	...	0.230787	0.244252	0.305447	-0.048815	-0.053898	0.013601	0.181662	-0.454110	0.498255	1.000000

	sum_sq	df	F	PR(>F)
C(Class)	1.340587e+05	2.0	298.275814	5.391536e-129
Residual	6.741005e+06	29997.0	NaN	NaN

	sum_sq	df	F	PR(>F)
C(Class)	1.661443e+05	2.0	1224.53601	0.0
Residual	2.034987e+06	29997.0	NaN	NaN

	sum_sq	df	F	PR(>F)
C(Distance_Group)	4.747145e+04	3.0	220.392802	1.969810e-141
Residual	2.153660e+06	29996.0	NaN	NaN

MSDS 7331 - Lab 3 - Airline Satisfaction Dataset¶

Data Understanding (20 points total)¶

[10 points] Describe the meaning and type of data (scale, values, etc.) for each attribute in the data file. Verify data quality: Are there missing values? Duplicate data? Outliers? Are those mistakes? How do you deal with these problems?¶

Check for NAs¶

Remove unwanted columns¶

Check distribution of the data¶

Summary of values to be used in classification modeling¶

[10 points] Visualize the any important attributes appropriately. Important: Provide an interpretation for any charts or graphs.¶

Two sample T Test for gender¶

Option A: Cluster Analysis¶

KNN Clustering with PCA¶

WCSS summary¶

PCA used to reduce dimensionality¶

Intepretation of Silhouette score of KNN Clustering¶

DBSCAN Clustering¶

Intepretation of Silhouette score of DBScan Clustering¶

Hierarchical Agglomerative Clustering (HAC) Clustering¶

Intepretation of Silhouette score of HAC Clustering¶

Deployment (10 points total)¶

Deployment Summary¶

Exceptional Work (10 points total)¶

Gausian Mixture¶

Step 1. Normalize the data¶

Step 2. AIC and BIC Testing on Normalized Data¶

Step 3. Further reduce dimensions through PCA¶

Step 4. AIC and BIC Testing on Normalized PCA Data¶

	Gender	Customer Type	Age	Type of Travel	Class	Flight Distance	Inflight wifi service	Departure/Arrival time convenient	Ease of Online booking	Gate location	...	TypeofTravelNumeric	ClassNumeric	SatisfactionNumeric	Survey_Total	Age_Group	Age_Group_Numeric	Distance_Group	Distance_Group_Numeric	Departure_Delay_Group	Departure_Delay_Group_Numeric
42798	Male	Loyal Customer	8	Business travel	Eco Plus	2586	2	5	5	5	...	0	1	0	36	Adolescent	1	Extra Long	4	Minimal	1
99439	Male	Loyal Customer	60	Business travel	Business	3262	1	1	1	1	...	0	2	1	46	Middle Age	3	Extra Long	4	Minimal	1
27324	Male	Loyal Customer	35	Personal Travel	Eco	259	3	1	3	4	...	1	0	0	37	Young Adult	2	Short	1	None	0
62959	Male	Loyal Customer	53	Business travel	Business	794	2	2	2	2	...	0	2	1	49	Middle Age	3	Moderate	2	Minimal	1
60767	Female	disloyal Customer	26	Business travel	Eco	784	3	3	3	5	...	0	0	0	42	Young Adult	2	Moderate	2	None	0
806	Female	Loyal Customer	26	Personal Travel	Eco	908	3	4	3	4	...	1	0	0	35	Young Adult	2	Moderate	2	None	0
30692	Male	Loyal Customer	50	Personal Travel	Eco	405	3	5	3	1	...	1	0	0	51	Middle Age	3	Short	1	Minimal	1
44695	Female	Loyal Customer	47	Business travel	Business	3506	4	4	4	4	...	0	2	1	44	Middle Age	3	Extra Long	4	Minimal	1
51878	Male	Loyal Customer	38	Business travel	Eco	231	3	2	2	2	...	0	0	0	39	Middle Age	3	Short	1	None	0
16194	Female	Loyal Customer	7	Personal Travel	Eco	209	5	3	5	4	...	1	0	1	49	Adolescent	1	Short	1	None	0
83004	Male	Loyal Customer	26	Business travel	Eco Plus	533	3	2	2	2	...	0	1	0	36	Young Adult	2	Moderate	2	None	0
96341	Male	Loyal Customer	53	Business travel	Business	2069	3	3	3	3	...	0	2	1	52	Middle Age	3	Long	3	None	0
41658	Female	Loyal Customer	62	Business travel	Business	3272	4	4	4	4	...	0	2	1	48	Middle Age	3	Extra Long	4	Minimal	1
33411	Male	Loyal Customer	57	Personal Travel	Eco	337	2	4	2	5	...	1	0	0	39	Middle Age	3	Short	1	None	0
38872	Male	Loyal Customer	54	Business travel	Business	3667	4	1	1	1	...	0	2	0	42	Middle Age	3	Extra Long	4	None	0
35012	Female	disloyal Customer	65	Business travel	Eco Plus	373	1	1	1	4	...	0	1	0	23	Middle Age	3	Short	1	Minimal	1
63879	Male	Loyal Customer	30	Business travel	Business	423	4	5	5	5	...	0	2	0	50	Young Adult	2	Short	1	Minimal	1
93161	Male	disloyal Customer	30	Business travel	Eco	377	2	2	2	4	...	0	0	0	44	Young Adult	2	Short	1	Minimal	1
102800	Male	Loyal Customer	33	Business travel	Business	525	5	5	5	5	...	0	2	1	52	Young Adult	2	Moderate	2	None	0
37013	Male	disloyal Customer	22	Business travel	Eco	1846	2	2	2	4	...	0	0	0	33	Young Adult	2	Long	3	Minimal	1
22720	Male	disloyal Customer	21	Business travel	Eco	230	5	3	5	5	...	0	0	1	40	Young Adult	2	Short	1	Minimal	1
35870	Male	Loyal Customer	13	Business travel	Business	954	3	3	3	3	...	0	2	1	45	Adolescent	1	Moderate	2	None	0
16044	Female	Loyal Customer	26	Business travel	Eco Plus	575	3	3	2	3	...	0	1	0	39	Young Adult	2	Moderate	2	None	0
95924	Male	Loyal Customer	33	Business travel	Business	598	3	3	3	3	...	0	2	1	47	Young Adult	2	Moderate	2	None	0
33563	Female	Loyal Customer	59	Personal Travel	Eco	944	4	2	3	3	...	1	0	1	38	Middle Age	3	Moderate	2	Minimal	1
24683	Male	Loyal Customer	19	Personal Travel	Eco	304	4	4	4	3	...	1	0	0	43	Young Adult	2	Short	1	Minimal	1
49016	Female	disloyal Customer	37	Business travel	Eco	720	3	3	3	1	...	0	0	0	32	Middle Age	3	Moderate	2	None	0
84076	Male	disloyal Customer	18	Business travel	Eco	1365	1	1	1	4	...	0	0	0	27	Young Adult	2	Long	3	None	0
5971	Male	Loyal Customer	59	Business travel	Eco	221	4	3	3	3	...	0	0	1	37	Middle Age	3	Short	1	None	0
102653	Male	disloyal Customer	26	Business travel	Business	1744	4	4	4	2	...	0	2	0	40	Young Adult	2	Long	3	None	0
31170	Female	Loyal Customer	47	Personal Travel	Eco Plus	453	3	4	3	3	...	1	1	0	45	Middle Age	3	Short	1	None	0
12672	Male	disloyal Customer	17	Business travel	Eco	370	4	5	4	3	...	0	0	1	51	Adolescent	1	Short	1	None	0
51107	Female	Loyal Customer	60	Business travel	Business	1145	5	5	5	5	...	0	2	1	64	Middle Age	3	Long	3	Minimal	1
74968	Female	Loyal Customer	62	Personal Travel	Eco	1919	5	4	5	4	...	1	0	1	45	Middle Age	3	Long	3	None	0
46611	Male	disloyal Customer	20	Business travel	Eco	1056	3	3	3	3	...	0	0	0	44	Young Adult	2	Long	3	Minimal	1
66407	Female	Loyal Customer	60	Business travel	Business	888	3	3	3	3	...	0	2	1	48	Middle Age	3	Moderate	2	None	0
83718	Male	Loyal Customer	60	Business travel	Eco Plus	1076	5	3	2	2	...	0	1	1	48	Middle Age	3	Long	3	None	0
35556	Female	Loyal Customer	19	Personal Travel	Business	547	3	2	3	3	...	1	2	0	41	Young Adult	2	Moderate	2	Minimal	1
53311	Female	disloyal Customer	20	Business travel	Eco	284	1	3	1	3	...	0	0	0	33	Young Adult	2	Short	1	Long	2
11252	Female	Loyal Customer	69	Personal Travel	Eco	341	2	5	2	3	...	1	0	0	40	Senior	4	Short	1	None	0
21211	Female	disloyal Customer	30	Business travel	Business	912	0	0	0	5	...	0	2	1	31	Young Adult	2	Moderate	2	None	0
51368	Male	Loyal Customer	52	Business travel	Business	3112	1	1	1	1	...	0	2	1	48	Middle Age	3	Extra Long	4	Minimal	1
99523	Female	disloyal Customer	22	Business travel	Eco	361	4	4	4	3	...	0	0	0	49	Young Adult	2	Short	1	None	0
83792	Female	Loyal Customer	54	Business travel	Business	2386	3	5	5	5	...	0	2	0	42	Middle Age	3	Long	3	Minimal	1
37433	Female	Loyal Customer	46	Business travel	Business	1620	4	4	4	4	...	0	2	1	54	Middle Age	3	Long	3	None	0
29894	Male	Loyal Customer	47	Business travel	Eco	429	5	2	2	2	...	0	0	1	47	Middle Age	3	Short	1	None	0
34124	Female	disloyal Customer	42	Business travel	Eco	776	3	3	3	3	...	0	0	0	34	Middle Age	3	Moderate	2	None	0
46624	Female	Loyal Customer	64	Business travel	Business	1709	0	0	0	2	...	0	2	1	38	Middle Age	3	Long	3	Minimal	1
3544	Male	Loyal Customer	55	Business travel	Business	1787	2	2	2	2	...	0	2	1	49	Middle Age	3	Long	3	Minimal	1
66706	Female	Loyal Customer	68	Personal Travel	Eco	746	3	4	2	3	...	1	0	0	50	Senior	4	Moderate	2	None	0

	sum_sq	df	F	PR(>F)
C(Age)	7.204341e+04	74.0	13.683684	1.190214e-161
Residual	2.129088e+06	29925.0	NaN	NaN

	sum_sq	df	F	PR(>F)
C(Departure_Delay_Group)	1.489027e+03	2.0	10.153092	0.000039
Residual	2.199643e+06	29997.0	NaN	NaN